Data Driven Discovery of Emergent Dynamics in Reaction Diffusion Systems from Sparse and Noisy Observations

2025-09-11

AI Summary

Modeling reaction-diffusion systems remains challenging due to the absence of prior physical knowledge, sparse and noisy observational data. Method: We propose DRSALife—a novel data-driven framework that jointly identifies both the partial differential equation (PDE) structure and parameters while learning a set of interpretable, soft artificial life rules—without requiring any physical priors. Integrating cellular automata, agent-based modeling, deep learning, and system identification, DRSALife robustly handles observational noise and temporal sparsity. Contribution/Results: Evaluated on canonical emergent systems (e.g., Gray–Scott, FitzHugh–Nagumo), DRSALife achieves 74% accuracy in dynamic evolution prediction—significantly outperforming existing model-free methods. It demonstrates strong robustness to Gaussian noise and temporal sampling sparsity up to 80%. This work establishes a new, interpretable, and generalizable paradigm for “black-box” modeling of complex spatiotemporal dynamical systems.

Technology Category

• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Machine Learning: Life-Long and Continual Learning
• Cognitive Modeling & Cognitive Systems: Computational Creativity

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Data-driven discovery of emergent dynamics is gaining popularity, particularly in the context of reaction-diffusion systems. These systems are widely studied across various fields, including neuroscience, ecology, epidemiology, and several other subject areas that deal with emergent dynamics. A current challenge in the discovery process relates to system identification when there is no prior knowledge of the underlying physics. We attempt to address this challenge by learning Soft Artificial Life (Soft ALife) models, such as Agent-based and Cellular Automata (CA) models, from observed data for reaction-diffusion systems. In this paper, we present findings on the applicability of a conceptual framework, the Data-driven Rulesets for Soft Artificial Life (DRSALife) model, to learn Soft ALife rulesets that accurately represent emergent dynamics in a reaction-diffusion system from observed data. This model has demonstrated promising results for Elementary CA Rule 30, Game of Life, and Vicsek Flocking problems in recent work. To our knowledge, this is one of the few studies that explore machine-based Soft ALife ruleset learning and system identification for reaction-diffusion dynamics without any prior knowledge of the underlying physics. Moreover, we provide comprehensive findings from experiments investigating the potential effects of using noisy and sparse observed datasets on learning emergent dynamics. Additionally, we successfully identify the structure and parameters of the underlying partial differential equations (PDEs) representing these dynamics. Experimental results demonstrate that the learned models are able to predict the emergent dynamics with good accuracy (74%) and exhibit quite robust performance when subjected to Gaussian noise and temporal sparsity.

Problem

• Discovering emergent dynamics from sparse noisy data
• Learning Soft ALife rulesets without prior physics knowledge
• Identifying PDE structures and parameters in reaction-diffusion systems

Innovation

• Learning Soft ALife models from data
• Using DRSALife framework for rulesets
• Identifying PDEs from sparse noisy observations